2024/07/09 by Lindner, Marko, Schmeckpeper, Dennis
#Condition number #Natural Sciences and Mathematics::510: Mathematics #Pseudospectrum #Spectral pollution #Stability
paper · doi:10.15480/882.13132
The stability of an approximating sequence (An) for an operator A usually requires, besides invertibility of A, the invertibility of further operators, say B,C,…, that are well-associated to the sequence (An). We study this set, A,B,C,…, of so-called stability indicators of (An) and connect it to the asymptotics of ‖An‖, ‖An−1‖ and κ(An)=‖An‖‖An−1‖ as well as to spectral pollution by showing that limsupSpecεAn=SpecεA∪SpecεB∪SpecεC∪…. We further specify, for each of ‖An‖, ‖An−1‖, κ(An) and SpecεAn, under which conditions even convergence applies.